Question

Find the equation of the line that is perpendicular to x - 3y = 6 and passes through the point (-2, -7)

Answer 1

Answer: y = -3x - 1

The steps to find the equation are as follow:
1. Find the slope
2. Plug the slope into the general equation, y = mx + c
3. Find the y-intercept
4. Plug the y-intercept into the equation we created in step 2
And that will give us the equation of the line

-------------------------------------------
Find the slope
-------------------------------------------
x - 3y = 6       ←Rearrange the equation to matches the format y = mx + c

3y = x - 6       ←divide by 3 through
÷3  ÷3  ÷3

y =1/3x - 2

Sope = 1/3

Slope of the perpendicular line = - 3 (negative reciprocal)

--------------------------------------------------------------------------------------
Plug in the value of the slope into the general equation y = mx + c
--------------------------------------------------------------------------------------
y = mx + c
y = -3x + c

--------------------------------------------------------------------------------------
Find the y-intercept
--------------------------------------------------------------------------------------
y = -3x + c

At coordinate (-2, -7)

-7 = 3(-2) + c          ←substitute x = -2 and y = -7

-7 = -6 + c              ← add 6 to both side
+6   +6

c = -1

--------------------------------------------------------------------------------------
Plug the value of the y-intercept into the equation y = -3x + c
--------------------------------------------------------------------------------------
y = -3x + c
y = -3x -1

--------------------------------------------------------------------------------------
Answer: y = -3x - 1
--------------------------------------------------------------------------------------